INTRODUCTION. 5 



with any one. A single fact, inconsistent with a 

 theory, may be sufficient to overturn it 



12. In tracing the necessary connection of na- 

 tural phenomena, this axiom is often of use : No- 

 thing exists in any state that is not determined by 

 some REASON to be in that state rather than in any 

 other. 



Hence, two things of which the conditions are deter- 

 mined by reasons that are precisely the same, are 

 in all respects similar to one another. Hence, al- 

 so, if there are two conditions, and no reason to 

 determine a subject to be in one of them rather 

 than another, we are to conclude that it is in nei- 

 ther. This axiom has been called the principle of 

 the SUFFICIENT REASON. It was used by ARCHI- 

 MEDES in his demonstration of some propositions in 

 mechanics; but it was first stated as a general 

 principle of philosophic reasoning by LEIBNITZ. It 

 may be used to great advantage for demonstrating 

 the more simple propositions of geometry as well as 

 of mechanics. 



13. Experiment is not only necessary in the in- 

 vestigation of truth, but it is useful for proving 

 truths that have already been investigated. 



In this latter application of it, it serves three pur- 

 poses: 



i. It verifies the conclusion of our reasonings, and dis- 

 covers whether any element has been left out, or 



any 



